What's the relationship between RMS framework and the Lorentz group?

In summary, the Robertson-Mansouri-Sexl framework is a well-known kinematic test theory for parameterizing deviations from Lorentz invariance. It is used to experimentally test for violations of Lorentz invariance, which is limited by group-theoretical theorems such as the Reciprocity Principle and the Lorentz Transformations. The underlying group structure of the RMS framework is still being studied and its relationship to the Lorentz group is not yet fully understood. However, it is an important tool for testing for violations of Lorentz invariance, which is a key concept in theoretical physics.
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What is the relationship between the Robertson-Mansouri-Sexl framework and the Lorentz group
The Robertson-Mansouri-Sexl framework, discussed in "Modern Tests of Lorentz Invariance", https://link.springer.com/article/10.12942/lrr-2005-5?affiliation, is "a well known kinematic test theory for parameterizing deviations from Lorentz invariance."

I'm a bit confused on the relationship between this framework, which tests experimentally for Lorentz invariance, and the group-theoretical theorems discussed in a recent thread that limit the theoretical possiblities for covariant formulations of physics, as discussed in this now-closed PF thread

https://www.physicsforums.com/threa...-postulate-or-assumption.1052965/post-6905619

in particular the (paywalled) paper "V. Berzi and V. Gorini, Reciprocity Principle and the Lorentz
Transformations, Jour. Math. Phys. 10, 1518 (1969)", https://doi.org/10.1063/1.1665000

I assume the RMS framework has some underlying group structure. The question is - is this underlying group structure the same or different than the Lorentz group? I've been perusing the Living Review article, which is rather long. Possibly it already contains the answer I seek, but I haven't been able to figure this out to my satisfaction. Unfortunately, I don't know enough group theory to answer the question myself from first principles :(.

A dumbed down version of the underlying and motivational question might be "If the Lorentz group and the Gallilean group are the only group-theoretical possibilities, what sort of test theory allows us to experimentally test for violations of Lorentz invariance?" The more specific question in the title of the thread is an attempt to answer this "fuzzier" question.
 
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FAQ: What's the relationship between RMS framework and the Lorentz group?

What is the RMS framework?

The RMS (Relativity, Mechanics, and Symmetry) framework is a theoretical construct used to study and analyze physical systems that exhibit relativistic properties. It integrates principles from special relativity, classical mechanics, and symmetry considerations to provide a comprehensive understanding of how physical laws transform under changes in reference frames.

What is the Lorentz group?

The Lorentz group consists of all Lorentz transformations, which are linear transformations that preserve the spacetime interval in special relativity. These transformations include rotations and boosts (changes in velocity) and form the mathematical foundation for describing how physical quantities transform between different inertial frames.

How does the RMS framework utilize the Lorentz group?

The RMS framework employs the Lorentz group to describe how physical systems behave under changes in reference frames. By using Lorentz transformations, the RMS framework ensures that the laws of physics remain invariant (unchanged) when switching between different inertial observers, thus adhering to the principles of special relativity.

Why is symmetry important in the RMS framework?

Symmetry is crucial in the RMS framework because it helps in identifying conserved quantities and invariant properties of physical systems. The Lorentz group, being a symmetry group, ensures that certain physical quantities (like the spacetime interval) remain unchanged under transformations. This invariance leads to conservation laws, such as the conservation of momentum and energy, which are fundamental in physics.

Can the RMS framework be applied to non-relativistic systems?

While the RMS framework is primarily designed for relativistic systems, it can be adapted to non-relativistic systems by considering the appropriate limits. For example, when velocities involved are much smaller than the speed of light, the Lorentz transformations reduce to Galilean transformations, which are used in classical mechanics. Thus, the RMS framework can provide insights into both relativistic and non-relativistic regimes.

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